Mechanical characterization of skeletal muscle myofibrils

Linking myosin heavy chain isoform shift to mechanical properties and fracture modes in skeletal muscle tissue

Muscle fibers play a crucial role in the mechanical action of skeletal muscle tissue. However, it is unclear how the histological variations affect the mechanical properties of tissues. In this study, the shift of myosin heavy chain (MHC) isoforms is used for the first time to establish a linkage between tissue histological variation and passive mechanical properties. The shift of MHC isoform is found not only to induce significant differences in skeletal muscle passive mechanical properties, but also to lead to differences in strain rate responses. Non-negligible rate dependence is observed even in the conventionally defined quasi-static regime. Fidelity in the estimated constitutive parameters, which can be impacted due to variation in MHC isoforms and hence in rate sensitivity, is enhanced using a Bayesian inference framework. Subsequently, scanning electron microscopy and fluorescence microscopy are used to characterize the fracture morphology of muscle tissues and fibers. The fracture mode of both MHC I and II muscle fibers exhibited shearing of endomysium. Results show that the increase in strain rate only leads to stronger rebounding of the muscle fibers during tissue rupture without changing fracture modes.

On multiscale tension-compression asymmetry in skeletal muscle

Skeletal muscle tissue shows a clear asymmetry with regard to the passive stresses under tensile and compressive deformation, referred to as tension-compression asymmetry (TCA). The present study is the first one reporting on TCA at different length scales, associated with muscle tissue and muscle fibres, respectively. This allows for the first time the comparison of TCA between the tissue and one of its individual components, and thus to identify the length scale at which this phenomenon originates. Not only the passive stress-stretch characteristics were recorded, but also the volume changes during the axial tension and compression experiments. The study reveals clear differences in the characteristics of TCA between fibres and tissue. At tissue level TCA increases non-linearly with increasing deformation and the ratio of tensile to compressive stresses at the same magnitude of strain reaches a value of approximately 130 at 13.5% deformation. At fibre level instead it initially drops to a value of 6 and then rises again to a TCA of 14. At a deformation of 13.5%, the tensile stress is about 6 times higher. Thus, TCA is about 22 times more expressed at tissue than fibre scale. Moreover, the analysis of volume changes revealed little compressibility at tissue scale whereas at fibre level, especially under compressive stress, the volume decreases significantly. The data collected in this study suggests that the extracellular matrix has a distinct role in amplifying the TCA, and leads to more incompressible tissue behaviour. STATEMENT OF SIGNIFICANCE: This article analyses and compares for the first time the tension-compression asymmetry (TCA) displayed by skeletal muscle at tissue and fibre scale. In addition, the volume changes of tissue and fibre specimens with application of passive tensile and compressive loads are studied. The study identifies a key role of the extracellular matrix in establishing the mechanical response of skeletal muscle tissue: It contributes significantly to the passive stress, it is responsible for the major part of tissue-scale TCA and, most probably, prevents/balances the volume changes of muscle fibres during deformation. These new results thus shed light on the origin of TCA and provide new information to be used in microstructure-based approaches to model and simulate skeletal muscle tissue.

Force Measurements From Myofibril to Filament

Contractility, the generation of force and movement by molecular motors, is the hallmark of all muscles, including striated muscle. Contractility can be studied at every level of organization from a whole animal to single molecules. Measurements at sub-cellular level are particularly useful since, in the absence of the excitation-contraction coupling system, the properties of the contractile proteins can be directly investigated; revealing mechanistic details not accessible in intact muscle. Moreover, the conditions can be manipulated with ease, for instance changes in activator Ca²⁺, small molecule effector concentration or phosphorylation levels and introducing mutations. Subcellular methods can be successfully applied to frozen materials and generally require the smallest amount of tissue, thus greatly increasing the range of possible experiments compared with the study of intact muscle and cells. Whilst measurement of movement at the subcellular level is relatively simple, measurement of force is more challenging. This mini review will describe current methods for measuring force production at the subcellular level including single myofibril and single myofilament techniques.

Mechano-geometrical skeletal muscle fibre characterisation under cyclic and relaxation loading

In the present work, mechano-geometrical characterisations of skeletal muscle fibres in two different deformation states, namely, axial tension and axial compression, were realised. In both cases, cyclic and relaxation tests were performed. Additionally, the changes in the volume of the fibres during deformation were recorded to obtain more detailed information about the muscle fibre load transfer mechanisms. To the best of the authors' knowledge, the present experimental investigation of the mechanical and geometrical characteristics of muscle fibres provides a novel comprehensive data set that can be used to obtain a better understanding of muscle fibre load transfer mechanisms and to construct meaningful models. In the present study, it is shown that muscle fibres exhibit incompressibility (5% volume decrease at maximum deformation) under tension and that this feature is more pronounced under compression loading (37% volume decrease at maximum deformation). These findings are particularly interesting and lead to a further understanding of load transfer mechanisms and to the development of new modelling strategies.

Investigating the passive mechanical behaviour of skeletal muscle fibres: Micromechanical experiments and Bayesian hierarchical modelling

Characterisation of the skeletal muscle's passive properties is a challenging task since its structure is dominated by a highly complex and hierarchical arrangement of fibrous components at different scales. The present work focuses on the micromechanical characterisation of skeletal muscle fibres, which consist of myofibrils, by realising three different deformation states, namely, axial tension, axial compression, and transversal compression. To the best of the authors' knowledge, the present study provides a novel comprehensive data set representing of different deformation states. These data allow for a better understanding of muscle fibre load transfer mechanisms and can be used for meaningful modelling approaches. As the present study shows, axial tension and compression experiments reveal a strong tension-compression asymmetry at fibre level. In comparison to the tissue level, this asymmetric behaviour is more pronounced at the fibre scale, elucidating the load transfer mechanism in muscle tissue and aiding in the development of future modelling strategies. Further, a Bayesian hierarchical modelling approach was used to consider the experimental fluctuations in a parameter identification scheme, leading to more comprehensive parameter distributions that reflect the entire observed experimental uncertainty. STATEMENT OF SIGNIFICANCE: This article examines for the first time the mechanical properties of skeletal muscle fibres under axial tension, axial compression, and transversal compression, leading to a highly comprehensive data set. Moreover, a Bayesian hierarchical modelling concept is presented to identify model parameters in a broad way. The results of the deformation states allow a new and comprehensive understanding of muscle fibres' load transfer mechanisms; one example is the effect of tension-compression asymmetry. On the one hand, the results of this study contribute to the understanding of muscle mechanics and thus to the muscle's functional understanding during daily activity. On the other hand, they are relevant in the fields of skeletal muscle multiscale, constitutive modelling.

Radial stiffness characteristics of the overlap regions of sarcomeres in isolated skeletal myofibrils in pre-force generating state

We have studied the stiffness of myofilament lattice in sarcomeres in the pre-force generating state, which was realized by a relaxing reagent, BDM (butane dione monoxime). First, the radial stiffness for the overlap regions of sarcomeres of isolated single myofibrils was estimated from the resulting decreases in diameter by osmotic pressure applied with the addition of Dextran. Then, the radial stiffness was also estimated from force-distance curve measurements with AFM technology. The radial stiffness for the overlap regions thus obtained was composed of a soft and a rigid component. The soft component visco-elastically changed in a characteristic fashion depending on the physiological conditions of myofibrils, suggesting that it comes from cross-bridge structures. BDM treatments significantly affected the soft radial component of contracting myofibrils depending on the approach velocity of cantilever: It was nearly equal to that in the contracting state at high approach velocity, whereas as low as that in the relaxing state at low approach velocity. However, comparable BDM treatments greatly suppressed the force production and the axial stiffness in contracting glycerinated muscle fibers and also the sliding velocity of actin filaments in the in vitro motility assay. Considering that BDM shifts the cross-bridge population from force generating to pre-force generating states in contracting muscle, the obtained results strongly suggest that cross-bridges in the pre-force generating state are visco-elastically attached to the thin filaments in such a binding manner that the axial stiffness is low but the radial stiffness significantly high similar to that in force generating state.

Upconverting Nanoparticles as Optical Sensors of Nano- to Micro-Newton Forces

Mechanical forces affect a myriad of processes, from bone growth to material fracture to touch-responsive robotics. While nano- to micro-Newton forces are prevalent at the microscopic scale, few methods have the nanoscopic size and signal stability to measure them in vivo or in situ. Here, we develop an optical force-sensing platform based on sub-25 nm NaYF₄ nanoparticles (NPs) doped with Yb³⁺, Er³⁺, and Mn²⁺. The lanthanides Yb³⁺ and Er³⁺ enable both photoluminescence and upconversion, while the energetically coupled d-metal Mn²⁺ adds force tunability through its crystal field sensitivity. Using a diamond anvil cell to exert up to 3.5 GPa pressure or ∼10 μN force per particle, we track stress-induced spectral responses. The red (660 nm) to green (520, 540 nm) emission ratio varies linearly with pressure, yielding an observed color change from orange to red for α-NaYF₄ and from yellow-green to green for d-metal optimized β-NaYF₄ when illuminated in the near infrared. Consistent readouts are recorded over multiple pressure cycles and hours of illumination. With the nanoscopic size, a dynamic range of 100 nN to 10 μN, and photostability, these nanoparticles lay the foundation for visualizing dynamic mechanical processes, such as stress propagation in materials and force signaling in organisms.

EFFECT OF LOADING RATE ON VISCOELASTIC PROPERTIES AND LOCAL MECHANICAL HETEROGENEITY OF FRESHLY ISOLATED MUSCLE FIBER BUNDLES SUBJECTED TO UNIAXIAL STRETCHING

To investigate the effect of viscoelastic behavior on instantaneous muscle mechanics, the passive mechanical properties for the range of physiologically relevant rates should be clarified. Therefore, a series of uniaxial extension tests were conducted at various stretching rates using the muscle fiber bundles, which contained extracellular matrix (ECM) and interfibrillar microstructural components. We revealed that the tensile strength is strain rate-sensitive over the examined range, i.e., the muscle fiber bundle failed at 109[Formula: see text][Formula: see text][Formula: see text]34, 122[Formula: see text][Formula: see text][Formula: see text]44, and 179[Formula: see text][Formula: see text][Formula: see text]61[Formula: see text]kPa (mean[Formula: see text][Formula: see text][Formula: see text]SD) for strain rates of 0.02, 0.1, and 0.5[Formula: see text]s[Formula: see text], respectively. Moreover, we found that the applied stretch was not distributed uniformly even in relaxed conditions; the ratio between maximum and minimum local strains within a specimen was 2–3 on average during stretching and increased up to approximately four just before failure, indicating local mechanical heterogeneity along a fiber bundle and its exaggeration by stretching. Macroscopically, however, the tensile strain at failure was almost constant, [Formula: see text]50%. The local heterogeneity of muscle strain distribution can lead to unstable oscillation in a computational model. Thus, in addition to the intrinsic viscous effects of the muscle fiber itself, those of ECM and interfibrillar microstructural components should be considered in mathematical modeling of skeletal muscle.

Velocities of unloaded muscle filaments are not limited by drag forces imposed by myosin cross-bridges

It is not known which kinetic step in the acto-myosin ATPase cycle limits contraction speed in unloaded muscles (V0). Huxley's 1957 model [Huxley AF (1957) Prog Biophys Biophys Chem 7:255-318] predicts that V0 is limited by the rate that myosin detaches from actin. However, this does not explain why, as observed by Bárány [Bárány M (1967) J Gen Physiol 50(6, Suppl):197-218], V0 is linearly correlated with the maximal actin-activated ATPase rate (vmax), which is limited by the rate that myosin attaches strongly to actin. We have observed smooth muscle myosin filaments of different length and head number (N) moving over surface-attached F-actin in vitro. Fitting filament velocities (V) vs. N to a detachment-limited model using the myosin step size d=8 nm gave an ADP release rate 8.5-fold faster and ton (myosin's attached time) and r (duty ratio) ∼10-fold lower than previously reported. In contrast, these data were accurately fit to an attachment-limited model, V=N·v·d, over the range of N found in all muscle types. At nonphysiologically high N, V=L/ton rather than d/ton, where L is related to the length of myosin's subfragment 2. The attachment-limited model also fit well to the [ATP] dependence of V for myosin-rod cofilaments at three fixed N. Previously published V0 vs. vmax values for 24 different muscles were accurately fit to the attachment-limited model using widely accepted values for r and N, giving d=11.1 nm. Therefore, in contrast with Huxley's model, we conclude that V0 is limited by the actin-myosin attachment rate.

Radial stability of the actomyosin filament lattice in isolated skeletal myofibrils studied using atomic force microscopy

The radial stability of the actomyosin filament lattice in skeletal myofibrils was examined by using atomic force microscopy. The diameter and the radial stiffness of the A-band region were examined based on force-distance curves obtained for single myofibrils adsorbed onto cover slips and compressed with the tip of a cantilever and with the Dextran treatment. The results obtained indicated that the A-band is composed of a couple of stiffness components having a rigid core-like component. It was further clarified that these radial components changed the thickness as well as the stiffness depending on the physiological condition of myofibrils. Notably, by decreasing the ionic strength, the diameter of the A-band region became greatly shrunken, but the rigid core-like component thickened, indicating that the electrostatic force distinctly affects the radial structure of actomyosin filament components. The results obtained were analyzed based on the elementary structures of the filament lattice composed of cross-bridges, thin filaments and thick filament backbones. It was clarified that the actomyosin filament lattice is radially deformable greatly and that (1), under mild compression, the filament lattice is stabilized primarily by the interactions of myosin heads with thin filaments and thick filament backbones, and (2), under severe compression, the electrostatic repulsive interactions between thin filaments and thick filament backbones became predominant.

A multisegmental cross-bridge kinetics model of the myofibril

Striated muscle is a mechanical system that develops force and generates power in serving vital activities in the body. Striated muscle is a complex biological system; a single mammalian muscle fibre contains up to hundred or even more myofibrils in parallel connected via an inter-myofibril filament network. In one single myofibril thousands of sarcomeres are lined up as a series of linear motors. We recently demonstrated that half-sarcomeres (hS) in a single myofibril operate non-uniformly. We outline a mathematical framework based on cross-bridge kinetics for the simulation of the force response and length change of individual hS in a myofibril. The model describes the muscle myofibril in contraction experiments under various conditions. The myofibril is modeled as a multisegmental mechanical system of hS models, which have active and viscoelastic properties. In the first approach, a two-state cross-bridge formalism relates the hS force to the chemical kinetics of ATP hydrolysis, as first described by Huxley [1957. Muscle structure and theories of contraction. Prog. Biophys. Mol. Biol. 7, 255-318]. Two possible types of biological variability are introduced and modeled. Numerical simulations of a myofibril composed of four to eight hS show a non-uniform hS length distribution and complex internal dynamics upon activation. We demonstrate that the steady-state approximation holds only in restricted time zones during activation. Simulations of myofibril contraction experiments that reproduce the classic steady-state force-length and force-velocity relationships, strictly constrained or "clamped" in either end-held isometric or isotonic contraction conditions, reveal a small but conspicuous effect of hS dynamics on force.

Nonlinear force-length relationship in the ADP-induced contraction of skeletal myofibrils

The regulatory mechanism of sarcomeric activity has not been fully clarified yet because of its complex and cooperative nature, which involves both Ca(2+) and cross-bridge binding to the thin filament. To reveal the mechanism of regulation mediated by the cross-bridges, separately from the effect of Ca(2+), we investigated the force-sarcomere length (SL) relationship in rabbit skeletal myofibrils (a single myofibril or a thin bundle) at SL > 2.2 microm in the absence of Ca(2+) at various levels of activation by exogenous MgADP (4-20 mM) in the presence of 1 mM MgATP. The individual SLs were measured by phase-contrast microscopy to confirm the homogeneity of the striation pattern of sarcomeres during activation. We found that at partial activation with 4-8 mM MgADP, the developed force nonlinearly depended on the length of overlap between the thick and the thin filaments; that is, contrary to the maximal activation, the maximal active force was generated at shorter overlap. Besides, the active force became larger, whereas this nonlinearity tended to weaken, with either an increase in [MgADP] or the lateral osmotic compression of the myofilament lattice induced by the addition of a macromolecular compound, dextran T-500. The model analysis, which takes into account the [MgADP]- and the lattice-spacing-dependent probability of cross-bridge formation, was successfully applied to account for the force-SL relationship observed at partial activation. These results strongly suggest that the cross-bridge works as a cooperative activator, the function of which is highly sensitive to as little as <or=1 nm changes in the lattice spacing.

Sarcomere dynamics during muscular contraction and their implications to muscle function

This article attempts to identify the key aspects of sarcomere inhomogeneity and the dynamics of sarcomere length changes in muscle contraction experiments and focuses on understanding the mechanics of myofibrils or muscle fibres when viewed as independent units of biological motors (the half-sarcomeres) connected in series. Muscle force generation has been interpreted traditionally on the basis of the kinetics of crossbridge cycling, i.e. binding of myosin heads to actin and consecutive force generating conformational change of the head, under controlled conditions and assuming uniformity of sarcomere or half-sarcomere behaviour. However, several studies have shown that re-distribution of internal strain within myofibrils and muscle fibres may be a key player, particularly, during stretch or relaxation so that force kinetics parameters are strongly affected by sarcomere dynamics. Here, we aim to shed light on how force generation, crossbridge kinetics, and the complex sarcomere movements are to be linked and which mechanical concepts are necessary to develop a comprehensive contraction model of a myofibril.

Passive stiffness of Drosophila IFM myofibrils: a novel, high accuracy measurement method

As the smallest muscle-cell substructure that retains the intact contractile apparatus, the single myofibril is considered the optimal specimen for muscle mechanics, although its small size also poses some technical difficulties. Myofibrils from Drosophila indirect flight muscle (IFM) are particularly difficult to study because their high passive stiffness makes them hard to handle, and too resistant to stretch to produce enough elongation for the accurate measurement of sarcomere length change. In this study, we devised a novel method for accurate stiffness measurement of single relaxed myofibrils using microfabricated cantilevers and phase contrast microscopy. A special experimental protocol was developed to minimize errors, and some data analysis strategies were used to identify and exclude spurious data. Remarkably consistent results were obtained from Drosophila IFM myofibrils. This novel, high accuracy method is potentially an effective tool for detecting small passive stiffness change in muscle mutants.

A new muscle contractile system composed of a thick filament lattice and a single actin filament

To bridge the gap between the contractile system in muscle and in vitro motility assay, we have devised an A-band motility assay system. A glycerinated skeletal myofibril was treated with gelsolin to selectively remove the thin filaments and expose a single A-band. A single bead-tailed actin filament trapped by optical tweezers was made to interact with the inside or the outer surface of the A-band, and the displacement of the bead-tailed filament was measured in a physiological ionic condition by phase-contrast and fluorescence microscopy. We observed large back-and-forth displacement of the filament accompanied by a large change in developed force. Despite this large tension fluctuation, we found that the average force was proportional to the overlap inside and outside the A-band up to approximately 150 nm and 300 nm from the end of the A-band, respectively. Consistent with the difference in the density of myosin molecules, the average force per unit length of the overlap inside the A-band (the time-averaged force/myosin head was approximately 1 pN) was approximately twice as large as that outside. Thus, we conclude that the A-band motility assay system described here is suitable for studying force generation on a single actin filament, and its sliding movement within a regular three-dimensional thick filament lattice.

Sarcomeric determinants of striated muscle relaxation kinetics

Ca2+ is the primary regulator of force generation by cross-bridges in striated muscle activation and relaxation. Relaxation is as necessary as contraction and, while the kinetics of Ca2+-induced force development have been investigated extensively, those of force relaxation have been both studied and understood less well. Knowledge of the molecular mechanisms underlying relaxation kinetics is of special importance for understanding diastolic function and dysfunction of the heart. A number of experimental models, from whole muscle organs and intact muscle fibres down to single myofibrils, have been used to explore the cascade of kinetic events leading to mechanical relaxation. By using isolated myofibrils and fast solution switching techniques we can distinguish the sarcomeric mechanisms of relaxation from those of myoplasmic Ca2+ removal. There is strong evidence that cross-bridge mechanics and kinetics are major determinants of the time course of striated muscle relaxation whilst thin filament inactivation kinetics and cooperative activation of thin filament by cycling, force-generating cross-bridges do not significantly limit the relaxation rate. Results in myofibrils can be explained well by a simple two-state model of the cross-bridge cycle in which the apparent rate of the force generating transition is modulated by fast, Ca2+-dependent equilibration between off- and on-states of actin. Inter-sarcomere dynamics during the final rapid phase of full force relaxation are responsible for deviations from this simple model.

Why choose myofibrils to study muscle myosin ATPase?

Our objective is to propose an overview of the usefulness of skeletal myofibril as an experimental system for studying mechanochemical coupling of skeletal muscles and myosin ATPase activity. The myofibril is a true functional mini-muscle that is able to contract in the presence of ATP. It also contains the machinery necessary for the calcium sensitivity of the contraction. In the absence of calcium, myofibrillar ATPase activity is basal, no shortening occurs and no active force is developed. In the presence of calcium, myofibrillar ATPase is activated and myofibrils either shorten with no external load (native myofibrils) or contract isometrically (cross-linked myofibrils). With this organised system, both chemical and mechanical studies can be carried out. For a decade, our laboratory has been using rabbit psoas myofibrils for exploring myosin ATPase activity. The first challenge was to successfully apply rapid kinetic approaches, such as rapid-flow-quench, to this organised system. Another challenge was to work with myofibrils in cryoenzymic conditions, i.e. in the presence of organic solvents and at sub-zero temperatures. In this overview, we highlight differences between the myosin ATPase in organised systems (myofibrils or fibres) and that of contractile proteins in solution (S1 or actoS1) that we observed using these approaches. We discuss the importance of these differences in terms of mechanochemical coupling. It is concluded that great care should be taken when extrapolating mechanochemical properties of the contractile proteins in solution to the whole muscle.

Inter-sarcomere dynamics in muscle fibres. A neglected subject?

The sarcomere is the functional unit of muscle, and all sarcomeres are connected in series in myofibrils within a muscle fibre. From this point of view of the structure a single model consisting of a contractile, a series and a parallel element can not account for the description of a real muscle fibre. Additionally, the titin protein filament needs to be considered as a passive visco-elastic element in parallel with the contractile apparatus. Therefore, the structure of a single muscle fibre is complex due mechanical elements ("motors") operating in series and in parallel. Moreover, variability does exist in the mechanical properties along a fibre and hence a multi-segmental model is more realistic and would give rise to many new insights. By attributing a segment model to each half-sarcomere, a fibre can be constructed through rigorous coupling of these units in series and parallel. The dynamics of such a multi-segmental model is much more complex, but it can explain a variety of effects reported in standard classical mechanics experiments. With a relatively simple mechanistic description we can show that the dynamics of such multi-sarcomere systems exhibit a variety of effects (relaxation phenomena, permanent extra-tension, biphasic force-velocity relation) and should therefore not be neglected in muscle fibre modelling. We have observed in single skinned fibre experiments that non-uniformities in sarcomere length changes are prominent during activation and relaxation.

Bio-Nanomuscle Project: Contractile Properties of Single Actin Filaments in an A-Band Motility Assay System

We have developed a new microscopic technique to measure the force generated on a single actin filament (FA) in the A-band in which the intact lattice structure composed of myosin thick filaments is maintained; we call this newly developed system "Bio-nanomuscle (or an A-band motility assay system)". The A-bands were prepared by selective removal of thin filaments from rabbit skeletal glycerinated myofibrils under optical microscope with the use of gelsolin (a severing and barbed (B)-end capping protein of FA) that was prepared from bovine serum. A polystyrene bead of 1 microm in diameter attached to the B-end of FA (through a gelsolin molecule attached to the surface of the bead) was trapped and manipulated with optical tweezers. The displacement of the bead up to 200 nm (corresponding to the force of approximately 40 pN) was determined by phase-contrast image analysis. At the initial stage of this study, the overlapping length of an FA with the A-band was determined from the fluorescence image of FA labeled with rhodamine-phalloidin (Rh-Ph) and the phase-contrast image, but we later improved the method of determination by moving the sample stage stepwise using the piezo actuator. The average force per overlap was subsequently estimated and the histogram was fitted with two Gaussian distributions. Each peak is supposed to correspond to the force developed by FA interacting outside or inside the A-band, and the peak value of the latter was estimated to be 140 pN/microm. From this value, the average force developed per each cross-bridge (CB; a two-headed myosin molecule) was determined to be 1.3 pN.

Characterization of the cross-bridge force-generating step using inorganic phosphate and BDM in myofibrils from rabbit skeletal muscles

The inhibitory effects of inorganic phosphate (P(i)) on isometric force in striated muscle suggest that in the ATPase reaction P(i) release is coupled to force generation. Whether P(i) release and the power stroke are synchronous events or force is generated by an isomerization of the quaternary complex of actomyosin and ATPase products (AM.ADP.P(i)) prior to the following release of P(i) is still controversial. Examination of the dependence of isometric force on [P(i)] in rabbit fast (psoas; 5-15 degrees C) and slow (soleus; 15-20 degrees C) myofibrils was used to test the two-step hypothesis of force generation and P(i) release. Hyperbolic fits of force-[P(i)] relations obtained in fast and slow myofibrils at 15 degrees C produced an apparent asymptote as [P(i)]-->infinity of 0.07 and 0.44 maximal isometric force (i.e. force in the absence of P(i)) in psoas and soleus myofibrils, respectively, with an apparent K(d) of 4.3 mM in both. In each muscle type, the force-[P(i)] relation was independent of temperature. However, 2,3-butanedione 2-monoxime (BDM) decreased the apparent asymptote of force in both muscle types, as expected from its inhibition of the force-generating isomerization. These data lend strong support to models of cross-bridge action in which force is produced by an isomerization of the AM.ADP.P(i) complex immediately preceding the P(i) release step.

Contractility of single myofibrils of rabbit skeletal muscle studied at various MgATP concentrations

A novel experimental method was developed to study the contractility of single myofibrils of skeletal muscle. Single myofibrils (ca. 1 microm in diameter) prepared from glycerinated rabbit psoas muscle were suspended between rigid and flexible microneedles by the entwining method. The length changes of the preparations applied via the rigid microneedle by an actuator and the force produced were measured by photo-electrically detecting the nanometer deflections of the flexible microneedle. Single myofibril preparations maintained uniform sarcomere striations during contraction-relaxation cycles. The isometric force produced, the velocity of unloaded shortening, and the force-velocity relationship of single myofibrils were investigated at various MgATP concentrations. The contractility of single myofibrils thus obtained in the absence of ATP regenerative systems was essentially the same as that of skinned muscle fibers under comparable conditions in the presence of ATP regenerative systems. Thus, it was found that (1) the present experimental method is useful for studying the contractility of single myofibrils, and (2) in single myofibril preparations, the MgATP concentration at actomyosin sites is well equilibrated with that in bathing solutions.

The effect of inorganic phosphate on force generation in single myofibrils from rabbit skeletal muscle

In striated muscle, force generation and phosphate (P(i)) release are closely related. Alterations in the [P(i)] bathing skinned fibers have been used to probe key transitions of the mechanochemical coupling. Accuracy in this kind of studies is reduced, however, by diffusional barriers. A new perfusion technique is used to study the effect of [P(i)] in single or very thin bundles (1-3 microM in diameter; 5 degrees C) of rabbit psoas myofibrils. With this technique, it is possible to rapidly jump [P(i)] during contraction and observe the transient and steady-state effects on force of both an increase and a decrease in [P(i)]. Steady-state isometric force decreases linearly with an increase in log[P(i)] in the range 500 microM to 10 mM (slope -0.4/decade). Between 5 and 200 microM P(i), the slope of the relation is smaller ( approximately -0.07/decade). The rate constant of force development (k(TR)) increases with an increase in [P(i)] over the same concentration range. After rapid jumps in [P(i)], the kinetics of both the force decrease with an increase in [P(i)] (k(Pi(+))) and the force increase with a decrease in [P(i)] (k(Pi(-))) were measured. As observed in skinned fibers with caged P(i), k(Pi(+)) is about three to four times higher than k(TR), strongly dependent on final [P(i)], and scarcely modulated by the activation level. Unexpectedly, the kinetics of force increase after jumps from high to low [P(i)] is slower: k(Pi(-)) is indistinguishable from k(TR) measured at the same [P(i)] and has the same calcium sensitivity.

Modulation by substrate concentration of maximal shortening velocity and isometric force in single myofibrils from frog and rabbit fast skeletal muscle

1. The effects of magnesium adenosine triphosphate (MgATP; also referred to as 'substrate') concentration on maximal force and shortening velocity have been studied at 5 C in single and thin bundles of striated muscle myofibrils. The minute diameters of the preparations promote rapid diffusional equilibrium between the bathing medium and lattice space so that during contraction fine control of substrate and product concentrations is achieved. 2. Myofibrils from frog tibialis anterior and rabbit psoas fast skeletal muscles were activated maximally by rapidly (10 ms) exchanging a continuous flux of pCa 8.0 for one at pCa 4.75 at a range of substrate concentrations from 10 microM to 5 mM. At high substrate concentrations maximal isometric tension and shortening velocity of both frog and rabbit myofibrils were very close to those determined in whole fibre preparations from the same muscle types. 3. As in frog and rabbit skinned whole fibres, the maximal isometric force of the myofibril preparations decreases as MgATP concentration is increased. The maximal velocity of unloaded shortening (V0) depends hyperbolically on substrate concentration. V0 extrapolated to infinite MgATP (3.6 +/- 0.2 and 0.8 +/- 0.03 l0 s-1 in frog and rabbit myofibrils, respectively) is very close to that determined directly at high substrate concentration. The Km is 210 +/- 20 microM for frog tibialis anterior and 120 +/- 10 microM for rabbit psoas myofibrils, values about half those found in larger whole fibre preparations of the same muscle types. This implies that measurements in whole skinned fibres are perturbed by diffusional delays, even in the presence of MgATP regenerating systems. 4. In both frog and rabbit myofibrils, the Km for V0 is about one order of magnitude higher than the Km for myofibrillar MgATPase determined biochemically in the same experimental conditions. This confirms that the difference between the Km values for MgATPase and shortening velocity is a basic feature of the mechanism of chemomechanical transduction in muscle contraction.

Calcium dependence of the apparent rate of force generation in single striated muscle myofibrils activated by rapid solution changes

Single myofibrils or small groups of myofibrils were isolated from different types of striated muscle: rabbit psoas, frog tibialis anterior, frog atrial and ventricular muscle. The Ca2+ concentration of the solution perfusing the myofibrils was changed within few milliseconds by translating the interface between two flowing streams of solution across the preparations. In all types of myofibrils tested, the time course of force rise in response to maximal activation (pCa 4.75) was approximately monoexponential and nearly superimposable on that observed after a release-restretch protocol applied to the myofibril at the plateau of maximal contractions. This suggests that the kinetics of force development following rapid myofibril activation essentially reflects the kinetics of interaction between contractile proteins. The half time of force rise in response to maximal activation varied among different myofibril types; it was shortest in frog tibialis anterior myofibrils and longest in frog ventricular myofibrils. In all types of myofibril preparations tested the half time of force rise increased with decreasing Ca2+ levels in the activating solution. The finding provides support for a kinetic mechanism of force regulation by Ca2+ in all types of striated muscle. The extent of this Ca2+ effect, however, varied among the different myofibril preparations tested; at 15 degrees C for instance, it was smaller in frog tibialis anterior myofibrils than in the other preparations.

ATPase and shortening rates in frog fast skeletal myofibrils by time-resolved measurements of protein-bound and free Pi

Shortening and ATPase rates were measured in Ca2+-activated myofibrils from frog fast muscles in unloaded conditions at 4 degrees C. ATPase rates were determined using the phosphate-binding protein method (free phosphate) and quench flow (total phosphate). Shortening rates at near zero load (V0) were estimated by quenching reaction mixtures 50 ms to 10 s old at pH 3.5 and measuring sarcomere lengths under the optical microscope. As with the rabbit psoas myofibrils (C. Lionne, F. Travers, and T. Barman, 1996, Biophys. J. 70:887-895), the ATPase progress curves had three phases: a transient Pi burst, a fast linear phase (kF), and a deceleration to a slow phase (kS). Evidence is given that kF is the ATPase rate of shortening myofibrils. V0 is in good agreement with mechanical measurements in myofibrils and fibers. Under the same conditions and at saturation in ATP, V0 and kF are 2.4 microm half-sarcomere(-1) s(-1) and 4.6 s(-1), and their Km values are 33 and 200 microM, respectively. These parameters are higher than found with rabbit psoas myofibrils. The myofibrillar kF is higher than the fiber ATPase rates obtained previously in frog fast muscles but considerably lower than obtained in skinned fibers by the phosphate-binding protein method (Z. H. He, R. K. Chillingworth, M. Brune, J. E. T. Corrie, D. R. Trentham, M. R. Webb, and M. R. Ferenczi, 1997, J. Physiol. 50:125-148). We show that, with frog as with rabbit myofibrillar ATPase, phosphate release is the rate-limiting step.

Probing the coupling of Ca2+ and rigor activation of rabbit psoas myofibrillar ATPase with ethylene glycol

We have exploited solvent perturbation to probe the coupling of Ca2+ and rigor activation of the ATPase of myofibrils from rabbit psoas. Three techniques were used: overall myofibrillar ATPases by the rapid-flow quench method; kinetics of the interaction of ATP with myofibrils by fluorescence stopped-flow; and myofibrillar shortening by optical microscopy. Because of its extensive use with muscle systems, ranging from myosin subfragment-1 to muscle fibres, we chose 40% ethylene glycol as the relaxing agent. At 4 degrees C, the glycol had little effect on the myofibrillar ATPase at low [Ca2+], but at high [Ca2+] the activity was reduced 50-fold, close to the level found under relaxing conditions, and there was no shortening. However, the ATPase of chemically cross-linked myofibrils (permanently activated even without Ca2+) was reduced only 3-4-fold. The lesser reduction of the ATPase of permanently activated myofibrils was also observed in single turnover experiments in which activation occurs by a few heads in the rigor state activating the remaining heads. The addition of ADP, which also promotes strong head-thin filament interactions, also activated the ATPase but only in the presence of Ca2+. Further experiments revealed that in 40% ethylene glycol, Ca2+ does initiate shortening but only with the aid of strong interactions and at temperatures above 15 degrees C. This confirms that in the organized and intact myofibril, Ca2+ and rigor activation are coupled, as proposed previously for regulated actomyosin subfragment-1.

Measurement of nucleotide release kinetics in single skeletal muscle myofibrils during isometric and isovelocity contractions using fluorescence microscopy

Rabbit psoas muscle myofibrils, in the presence of the fluorescent nucleotide analog 2'(3')-O-[N-[2-[[Cy3]amido]ethyl]carbamoyl]-adenosine 5' triphosphate (Cy3-EDA-ATP), showed selective fluorescence staining of the A-band with a reduced fluorescence at the M-line. Addition of Cy3-EDA-ATP to a myofibril in the presence of Ca2+ caused auxotonic shortening against a compliant glass microneedle. These results indicate that Cy3-EDA-ATP is a substrate for myosin in the myofibril system. The kinetics of nucleotide release from a single myofibril, held isometrically between two needles, were measured by the displacement of prebound Cy3-EDA-ATP on flash photolysis of caged ATP. The A-band fluorescence of the myofibril decayed exponentially with a rate constant of 0.3 s(-1) at 8 degrees C, an order of magnitude faster than that for isolated thick filaments in the absence of actin. When a myofibril was imposed to shorten with a constant velocity by a piezoelectric actuator, the nucleotide displacement rate constant initially increased to 0.7 s(-1) with increasing shortening velocity and then declined with a further increase in shortening velocity. These results demonstrate that the displacement rates of Cy3-EDA-nucleotides bound to the cross-bridges in the contracting myofibril reflect a process that shows strain dependence.

Actin-titin interaction in cardiac myofibrils: probing a physiological role

The high stiffness of relaxed cardiac myofibrils is explainable mainly by the expression of a short-length titin (connectin), the giant elastic protein of the vertebrate myofibrillar cytoskeleton. However, additional molecular features could account for this high stiffness, such as interaction between titin and actin, which has previously been reported in vitro. To probe this finding for a possible physiological significance, isolated myofibrils from rat heart were subjected to selective removal of actin filaments by a calcium-independent gelsolin fragment, and the "passive" stiffness of the specimens was recorded. Upon actin extraction, stiffness decreased by nearly 60%, and to a similar degree after high-salt extraction of thick filaments. Thus actin-titin association indeed contributes to the stiffness of resting cardiac muscle. To identify possible sites of association, we employed a combination of different techniques. Immunofluorescence microscopy revealed that actin extraction increased the extensibility of the previously stiff Z-disc-flanking titin region. Actin-titin interaction within this region was confirmed in in vitro cosedimentation assays, in which multimodule recombinant titin fragments were tested for their ability to interact with F-actin. By contrast, such assays showed no actin-titin-binding propensity for sarcomeric regions outside the Z-disc comb. Accordingly, the results of mechanical measurements demonstrated that competition with native titin by recombinant titin fragments from Z-disc-remote, I-band or A-band regions did not affect passive myofibril stiffness. These results indicate that it is actin-titin association near the Z-disc, but not along the remainder of the sarcomere, that helps to anchor the titin molecule at its N-terminus and maintain a high stiffness of the relaxed cardiac myofibril.

Active and passive forces of isolated myofibrils from cardiac and fast skeletal muscle of the frog

1. Force measurements in isolated myofibrils (15 degrees C; sarcomere length, 2.10 microns) were used in this study to determine whether sarcomeric proteins are responsible for the large differences in the amounts of active and passive tension of cardiac versus skeletal muscle. Single myofibrils and bundles of two to four myofibrils were prepared from glycerinated tibialis anterior and sartorius muscles of the frog. Skinned frog atrial myocytes were used as a model for cardiac myofibrils. 2. Electron microscope analysis of the preparations showed that: (i) frog atrial myocytes contained a small and variable number of individual myofibrils (from 1 to 7); (ii) the mean cross-sectional area and mean number of myosin filaments of individual cardiac myofibrils did not differ significantly from those of single skeletal myofibrils; and (iii) the total myofibril cross-sectional area of atrial myocytes was on average comparable to that of bundles of two to four skeletal myofibrils. 3. In maximally activated skeletal preparations, values of active force ranged from 0.45 +/- 0.03 microN for the single myofibrils (mean +/- S.E.M.; n = 16) to 1.44 +/- 0.24 microN for the bundles of two to four myofibrils (n = 9). Maximum active force values of forty-five cardiac myocytes averaged 1.47 +/- 0.10 microN and exhibited a non-continuous distribution with peaks at intervals of about 0.5 microN. The results suggest that variation in active force among cardiac preparations mainly reflects variability in the number of myofibrils inside the myocytes and that individual cardiac myofibrils develop the same average amount of force as single skeletal myofibrils. 4. The mean sarcomere length-resting force relation of atrial myocytes could be superimposed on that of bundles of two to four skeletal myofibrils. This suggests that, for any given amount of strain, individual cardiac and skeletal sarcomeres bear essentially the same passive force. 5. The length-passive tension data of all preparations could be fitted by an exponential equation. Equation parameters obtained for both types of myofibrils were in reasonable agreement with those reported for larger preparations of frog skeletal muscle but were very different from those estimated for multicellular frog atrial preparations. It is concluded that myofibrils are the major determinant of resting tension in skeletal muscle; structures other than the myofibrils are responsible for the high passive stiffness of frog cardiac muscle.